• Title, Summary, Keyword: Decay Function

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DECAY OF TURBULENCE IN FLUIDS WITH POLYTROPIC EQUATIONS OF STATE

  • Lim, Jeonghoon;Cho, Jungyeon
    • Journal of The Korean Astronomical Society
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    • v.53 no.2
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    • pp.49-57
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    • 2020
  • We present numerical simulations of decaying hydrodynamic turbulence initially driven by solenoidal (divergence-free) and compressive (curl-free) drivings. Most previous numerical studies for decaying turbulence assume an isothermal equation of state (EOS). Here we use a polytropic EOS, P ∝ ργ, with polytropic exponent γ ranging from 0.7 to 5/3. We mainly aim at determining the effects of γ and driving schemes on the decay law of turbulence energy, E ∝ t. We additionally study probability density function (PDF) of gas density and skewness of the distribution in polytropic turbulence driven by compressive driving. Our findings are as follows. First of all, we find that even if γ does not strongly change the decay law, the driving schemes weakly change the relation; in our all simulations, turbulence decays with α ≈ 1, but compressive driving yields smaller α than solenoidal driving at the same sonic Mach number. Second, we calculate compressive and solenoidal velocity components separately and compare their decay rates in turbulence initially driven by compressive driving. We find that the former decays much faster so that it ends up having a smaller fraction than the latter. Third, the density PDF of compressively driven turbulence with γ > 1 deviates from log-normal distribution: it has a power-law tail at low density as in the case of solenoidally driven turbulence. However, as it decays, the density PDF becomes approximately log-normal. We discuss why decay rates of compressive and solenoidal velocity components are different in compressively driven turbulence and astrophysical implication of our findings.

Measurement of Joint Resistance of $(Bi,Pb)_2Sr_2Ca_2Cu_3O_x$/Ag Superconducting Tape by Field decay Technique (자장감쇠법을 이용한 $(Bi,Pb)_2Sr_2Ca_2Cu_3O_x$/Ag 초전도선재의 접합저항 측정)

  • Kim, Jung-Ho;Lee, Seung-Muk;Joo, Jin-Ho
    • Progress in Superconductivity
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    • v.14 no.1
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    • pp.1-10
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    • 2012
  • We fabricated a closed coils by using resistive-joint method and the joint resistance of the coils were estimated by field decay technique in liquid nitrogen. We used the Runge-kutta method for the numerical analysis to calculate the decay properties. The closed coil was wound by $(Bi,Pb)_2Sr_2Ca_2Cu_3O_x$/Ag tape. Both ends the tape were overlapped and soldered to each other. The current was induced in a closed coils by external magnetic flux density. Its decay characteristic was observed by means of measuring the magnetic flux density generated by induced current at the center of the closed coil with hall sensor. The joint resistance was calculated as the ratio of the inductance of the loop to the time constants. The joint resistances were evaluated as a function of critical current of loop, contact length, sweep time, and external magnetic flux density in a contact length of 7 cm. It was observed that joint resistance was dependent on contact length of a closed coil, but independent of critical current, sweep time, and external magnetic flux density. The joint resistance was measured to be higher for a standard four-probe method, compared with that for the field decay technique. This implies that noise of measurement in a standard four-probe method is larger than that of field decay technique. It was estimated that joint resistance was $8.0{\times}10^{-9}{\Omega}$ to $11.4{\times}10^{-9}{\Omega}$ for coils of contact length for 7 cm. It was found that 40Pb/60Sn solder are unsuitable for persistent mode.

Experimental Study on Removal Characteristics of Indoor Suspended Particulates by Ventilation. (환기에 의한 실내 부유오염입자 제거특성에 관한 실험적 연구)

  • Kang, Tae-Wook
    • Journal of the Korean Solar Energy Society
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    • v.25 no.4
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    • pp.133-139
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    • 2005
  • In this paper, the ventilation performance of suspended particulates in indoor side was investigated by step-down method. Experiments were performed in function of mechanical ventilation types and locations of supply and extract air. The type 2 ventilation system shows the highest removal characteristics rather than other 2 types. It means that the displacement ventilation has also good decay rates of concentration compared to mixing ventilation.

STABILIZATION FOR THE VISCOELASTIC KIRCHHOFF TYPE EQUATION WITH A NONLINEAR SOURCE

  • Kim, Daewook
    • East Asian mathematical journal
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    • v.32 no.1
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    • pp.117-128
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    • 2016
  • In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

GLOBAL SOLUTION AND BLOW-UP OF LOGARITHMIC KLEIN-GORDON EQUATION

  • Ye, Yaojun
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.281-294
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    • 2020
  • The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.

FRF Distortion Caused by Exponential Window Function on Impact Hammer Testing and Its Solution (지수창함수를 사용한 임팩트햄머 실험에서 주파수응답함수의 왜곡과 개선책)

  • 안세진;정의봉
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.13 no.5
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    • pp.334-340
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    • 2003
  • Exponential window function Is widely used In impact hammer testing to reduce leakage error as well as to get a good S/N ratio. The larger its decaying rate is, the more effectively the leakage errors are reduced. But if the decay rate of the exponential window is too large, the FRF is distorted. And the modal parameters of the system can not be exactly identified by modal analysis technique. Therefore, it is a difficult problem to determine proper decay rate in impact hammer testing. In this paper, amount of the FRF distortion caused by exponential window is theoretically uncovered. A new circle fitting method is also proposed so that the modal parameters are directly extracted from impulse response spectrum distorted by the exponential-windowed impulse response data. The results by the conventional and proposed circle fitting method are compared through a numerical example.

Waves propagating in railway tracks at high frequencies (철로를 따라 장거리 전파하는 고주파수 대역 파동 특성 연구)

  • Ryue, J.;Thompson, D.J.;White, P.R.
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.791-796
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    • 2011
  • In order to understand long range wave propagation in railway tracks, it is required to identify how far vibrations can travel along a rail. To answer this question, the attenuation characteristics of the main propagating waves are required as a function of distance. In this work, it is identified which wave types predominantly propagate on various regions of the rail cross-section. Then decay rates of propagating waves in railway tracks are investigated for frequencies up to 80 kHz. A numerical method called the Wavenumber Finite Element (WFE) method is utilized to predict dispersion curves and decay rates for a rail on a continuous foundation. In order to validate the simulated results, measurements have been performed on a test track and an operational railway track. The measured results are compared with the output of the simulations and good agreements are found between them.

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Structural design concept of the forced-draft sodium-to-air heat exchanger in the decay heat removal system of PGSFR (소듐냉각고속로 잔열제거계통 강제대류 소듐-공기 열교환기의 구조개념 설계)

  • Kim, Nak Hyun;Lee, Sa Yong;Kim, Sung Kyun
    • Transactions of the Korean Society of Pressure Vessels and Piping
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    • v.12 no.1
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    • pp.78-84
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    • 2016
  • The FHX (Forced-draft sodium-to-air Heat Exchanger) employed in the ADHRS (active decay heat removal system) is a shell-and-tube type counter-current flow heat exchanger with M-shape finned-tube arrangement. Liquid sodium flows inside the heat transfer tubes and atmospheric air flows over the finned tubes. The unit is placed in the upper region of the reactor building and has function of dumping the system heat load into the final heat sink, i.e., the atmosphere. Heat is transmitted from the primary cold sodium pool into the ADHRS sodium loop via DHX (decay heat exchanger), and a direct heat exchange occurs between the tube-side sodium and the shell-side air through the FHX tube wall. This paper describes the DHRS and the structural design of the FHX.

Analytical Solutions for a Three-Member Decay Chain of Radionuclides Transport in a Single Fractured Porous Rock (단일균열 다공성암반에서 방사성핵종의 수송에 대한 3단계 붕괴사슬의 해석해)

  • Yu, Young-Woo;Chung, Chang-Hyun;Kim, Chang-Lak
    • Nuclear Engineering and Technology
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    • v.26 no.4
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    • pp.453-460
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    • 1994
  • The migration equation is modified for a three-member decay chain in the fracture and porous matrix Analytical solutions are obtained by utilizing Laplace transform the initial conditions of Delta function and Bateman equation. The concentrations for each nuclide of Np$^{237}$ -U$^{233}$ -Th$^{229}$ and U$^{234}$ -Th$^{230}$ -Ra$^{226}$ chains selected from the 4n+1 and 4n+2 chains are plotted by utilizing analytical solutions in the fracture. Retardation coefficient of the nuclides are obtained using those of the granite. The results indicate that the daughter nuclides such as U$^{233}$ , Th$^{229}$ , Th$^{230}$ and Ra$^{226}$ become important at the far field from the repository though there is very small initial inventory in the waste solid or spent fuel, for they are produced by the mother nuclides decayed in the fracture and porous matrix.

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